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A112218 McKay-Thompson series of class 102a for the Monster group. 1
1, 1, 0, 1, 0, 1, 1, 1, 1, 2, 1, 2, 3, 2, 2, 4, 3, 4, 5, 5, 5, 7, 6, 7, 9, 9, 9, 12, 11, 13, 15, 15, 16, 20, 19, 22, 25, 26, 27, 33, 32, 36, 41, 42, 44, 52, 52, 57, 64, 66, 70, 81, 82, 89, 99, 103, 109, 123, 125, 136, 150, 156, 165, 185, 189, 204, 223, 233, 247, 273, 281, 302 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..2500

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of sqrt(2 + T51A) in powers of q, where T51A = A058704. - G. C. Greubel, Jul 02 2018

a(n) ~ exp(2*Pi*sqrt(2*n/51)) / (2^(3/4) * 51^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 02 2018

EXAMPLE

T102a = 1/q +q +q^5 +q^9 +q^11 +q^13 +q^15 +2*q^17 +q^19 +...

MATHEMATICA

QP := QPochhammer; nmax = 100; f[x_, y_] := QP[-x, x*y]*QP[-y, x*y]*QP[x*y, x*y]; G[x_] := f[-x^2, -x^3]/f[-x, -x^2]; H[x_] := f[-x, -x^4]/f[-x, -x^2]; A := G[x^17]*G[x^3] + x^4*H[x^17]*H[x^3]; B := G[x^51]*H[x] - x^10*H[x^51]*G[x]; T51A := (A*B)/x; a:= CoefficientList[ Series[(x*(2 + T51A) + O[x]^nmax)^(1/2), {x, 0, nmax}], x]; Table[a[[n]], {n, 1, nmax}] (* G. C. Greubel, Jul 02 2018 *)

CROSSREFS

Sequence in context: A302257 A320387 A304707 * A172366 A132148 A237829

Adjacent sequences:  A112215 A112216 A112217 * A112219 A112220 A112221

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved

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Last modified January 16 06:59 EST 2019. Contains 319188 sequences. (Running on oeis4.)